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Simplifying 3x2 + -42x + 40 = 0 Reorder the terms: 40 + -42x + 3x2 = 0 Solving 40 + -42x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13.33333333 + -14x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -14x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -14x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -14x + x2 = 0 + -13.33333333 -14x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -14x + x2 = -13.33333333 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -13.33333333 + 49 Reorder the terms: 49 + -14x + x2 = -13.33333333 + 49 Combine like terms: -13.33333333 + 49 = 35.66666667 49 + -14x + x2 = 35.66666667 Factor a perfect square on the left side: (x + -7)(x + -7) = 35.66666667 Calculate the square root of the right side: 5.972157623 Break this problem into two subproblems by setting (x + -7) equal to 5.972157623 and -5.972157623.Subproblem 1
x + -7 = 5.972157623 Simplifying x + -7 = 5.972157623 Reorder the terms: -7 + x = 5.972157623 Solving -7 + x = 5.972157623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.972157623 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.972157623 + 7 x = 5.972157623 + 7 Combine like terms: 5.972157623 + 7 = 12.972157623 x = 12.972157623 Simplifying x = 12.972157623Subproblem 2
x + -7 = -5.972157623 Simplifying x + -7 = -5.972157623 Reorder the terms: -7 + x = -5.972157623 Solving -7 + x = -5.972157623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.972157623 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.972157623 + 7 x = -5.972157623 + 7 Combine like terms: -5.972157623 + 7 = 1.027842377 x = 1.027842377 Simplifying x = 1.027842377Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.972157623, 1.027842377}
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